Disjoining Pressure Research Articles

A general model for spin coating on a non-axisymmetric curved substrate

We derive a generalised asymptotic model for the flow of a thin fluid film over an arbitrarily parameterised non-axisymmetric curved substrate surface based on the lubrication approximation. In addition to surface tension, gravity and centrifugal force, our model incorporates the effects of the Coriolis force and disjoining pressure, together with a non-uniform initial condition, which have not been widely considered in existing literature. We use this model to investigate the impact of the Coriolis force and fingering instability on the spreading of a non-axisymmetric spin-coated film at a range of substrate angular velocities, first on a flat substrate, and then on parabolic cylinder- and saddle-shaped curved substrates. We show that, on flat substrates, the Coriolis force has a negligible impact at low angular velocities, and at high angular velocities results in a small deflection of fingers formed at the contact line against the direction of substrate rotation. On curved substrates, we demonstrate that, as the angular velocity is increased, spin-coated films transition from being dominated by gravitational drainage with no fingering to spreading and fingering in the direction with the greatest component of centrifugal force tangent to the substrate surface. For both curved substrates and all angular velocities considered, we show that the film thickness and total wetted substrate area remain similar over time to those on a flat substrate, with the key difference being the shape of the spreading droplet.

Flowerlike Spreading of Micellar Films during Emulsion Drop Evaporation.

We investigated the film spreading during the evaporation of submillimeter oil-in-water emulsion droplets on a solid surface, and observed a novel phenomenon where the film follows a two-layer spreading. In combination with the instability at the film front, the spreading front acquires a flowerlike pattern. The emergence of the two-layer structure is attributed to micelles within the oil film that yield an oscillating disjoining pressure. By considering both the slipping condition and the disjoining pressure, a scaling analysis is carried out that agrees well with the observed film spreading dynamics. The film spreading follows Tanner's law initially, while it becomes faster at a later stage, where the film radius follows r∼t^{1/2} for weak slip and r∼t^{3/8} for strong slip conditions.

Linear stability theory and molecular simulations of nanofilm dewetting with disjoining pressure, strong liquid–solid slip and thermal fluctuations

The dewetting of thin nanofilms is significantly affected by thermal fluctuations, liquid–solid slip and disjoining pressure, which can be described by lubrication equations augmented by appropriately scaled noise terms, known as stochastic lubrication equations. Here molecular dynamics simulations along with a newly proposed slip-generating method are adopted to study the instability of nanofilms with arbitrary slip. These simulations show that strong-slip dewetting is distinct from weak-slip dewetting by faster growth of perturbations and fewer droplets after dewetting, which cannot be predicted by the existing stochastic lubrication equation. A new stochastic lubrication equation considering the strong-slip boundary condition is thus derived using a long-wave approximation to the equations of fluctuating hydrodynamics. The linear stability analysis of this equation, i.e. surface spectrum, agrees well with molecular simulations. Interestingly, strong slip can break down the usual Stokes limits adopted in weak-slip dewetting and bring the inertia into effect. The evolution of the standard deviation of the film height $W^2(t)={\overline {h^2}-{\bar {h}}^2}$ at the initial stage of the strong-slip dewetting is found to be $W\sim t^{1/4}$ in contrast to $W\sim t^{1/8}$ for the weak-slip dewetting.

Collision of liquid drops: bounce or merge?

Whether colliding drops will merge with or bounce off each other is critical to numerous processes, and the physics involved is notoriously complex. In particular, experiments show that both sufficiently slow and fast head-on drop collisions lead to merging, but that there is often an intermediate regime in which bouncing is observed; these transitions in behaviour were recently discovered to be surprisingly sensitive to the radius of the drops and the ambient gas pressure. We show here that these transitions between bouncing and merging are governed by nanoscale phenomena; namely, gas-kinetic and disjoining pressure effects. To capture these crucial effects, a novel, open-source computational model is developed for the simulation of colliding drops. The model uses a hybrid approach, based on solving the Navier–Stokes equations in the drop with a lubrication approach for the unconventional physics of the gas film. Our simulations show remarkably good agreement with experiments of head-on collisions and also provide new experimentally verifiable predictions.

A comprehensive study of the enhanced oil recovery potential of low-salinity water in heavy oil sandstone reservoir

To determine the enhanced oil recovery potential of low-salinity brine for a heavy oil sandstone reservoir, a holistic approach including both experimental and theoretical studies was employed in this study. Macro-scale forced and spontaneous imbibition tests were performed to quantify the oil recovery potential by our considered three brines. Furthermore, micro-scale experiments, including FTIR (Fourier-Transform Infrared Spectroscopy), TGA (Thermogravimetric Analysis) and zeta potential, were executed to explore the micro-scale oil-brine-rock interactions (i.e., polar component desorption from the rock surface) that has controlled the macro-scale oil recovery efficiency. In addition, to further investigate the underlying physical mechanism that leads to the discrepancy in polar component desorption when subjected to different brines, charge-distribution multi-site complexation model (CD-MUSIC) and DLVO-based disjoining pressure calculation were performed to describe the molecular-level electrokinetic interactions at the oil-brine and rock-brine interfaces, as well as the total interaction force between these two interfaces. Our results show that the oil recovery efficiency of the low-salinity aquifer water (LSAW) was markedly higher than produced water (PW) and seawater (SW) from the forced and spontaneous imbibition tests. Combined with the marginal difference on interfacial tension (IFT) results, it guided us to conclude that the micro-scale oil-brine-rock interaction controlled the macro-scale oil recovery performance. FTIR and TGA experimental results on pristine quartz, oil aged quartz, as well as different water treated aged quartz powders revealed that the polar component desorption efficiency in different brines followed the order of LSAW > PW > SW, which was consistent with the macro-scale oil recovery trend. The total disjoining pressure result gave rise to the conclusion that the most repulsive disjoining pressure in LSAW leads to the most efficient desorption of polar oil component from the rock surface. In addition, the electrokinetic properties of the oil/brine and rock/brine interfaces, as well as the consequent electrical double layer force play a crucial role in differentiating the oil-brine-rock interactions in different brines. This study has shed light on the further application of low-salinity aquifer water in our target heavy oil reservoir.

Electrostatic interactions between soft nanoparticles beyond the Derjaguin approximation: Effects of finite size of ions and charges, dielectric decrement and ion correlations

HypothesisElectrostatic interactions between colloids are governed by the overlap of their electric double layers (EDLs) and the ionic screening of the structural charges distributed at their core surface and/or in their peripheral ion-permeable shell, relevant to soft particles like polymer colloids and microorganisms. Whereas ion size-mediated effects on the organization of isolated EDLs have been analysed, their contribution to the electrostatic energy of interacting soft particles has received less attention Theory and simulationsHerein, we elaborate a formalism to evaluate the electrostatic interaction energy profile between spherical core/shell particles, building upon a recent Poisson-Boltzmann theory corrected for the sizes of ions and particle structural charges, for ion correlations and dielectric decrement. Interaction energy is derived from pairwise disjoining pressure and exact Surface Element Integration method, beyond the Derjaguin approximation. The theory is sufficiently flexible to tackle homo- and hetero-interactions that involve weakly to highly charged hard, porous or core/shell nano- to micro-sized particles in asymmetric multivalent electrolytes. FindingsResults illustrate how ion steric effects, ion correlations and dielectric decrement impact the sign, magnitude and range of the interactions depending on the particle size, the Debye length, and the geometric and electrostatic properties of the particle core and shell components.

Theory of electrotuneable mechanical force of solid-liquid interfaces: A self-consistent treatment of short-range van der Waals forces and long-range electrostatic forces.

Elucidating the mechanical forces between two solid surfaces immersed in a communal liquid environment is crucial for understanding and controlling adhesion, friction, and electrochemistry in many technologies. Although traditional models can adequately describe long-range mechanical forces, they require substantial modifications in the nanometric region where electronic effects become important. A hybrid quantum-classical model is employed herein to investigate the separation-dependent disjoining pressure between two metal surfaces immersed in an electrolyte solution under potential control. We find that the pressure between surfaces transits from a long-range electrostatic interaction, attractive or repulsive depending on the charging conditions of surfaces, to a strong short-range van der Waals attraction and then an even strong Pauli repulsion due to the redistribution of electrons. The underlying mechanism of the transition, especially the attractive-repulsive one in the short-range region, is elucidated. This work contributes to the understanding of electrotunable friction and lubrication in a liquid environment.

Is it possible to overheat ice? The activated melting of TIP4P/Ice at solid–vapour coexistence.

A widely accepted phenomenological rule states that solids with free surfaces cannot be overheated. In this work we discuss this statement critically under the light of the statistical thermodynamics of interfacial roughening transitions. Our results show that the basal face of ice as described by the TIP4P/Ice model can remain mechanically stable for more than one hundred nanoseconds when overheated by 1 K, and for several hundreds of nanoseconds at smaller overheating despite the presence of a significant quasi-liquid layer at the surface. Such time scales, which are often of little experimental significance, can become a concern for the determination of melting points by computer simulations using the direct coexistence method. In the light of this observation, we reinterpret computer simulations of ice premelting and show that current results for the TIP4P/Ice model all imply a scenario of incomplete surface melting. Using a thermodynamic integration path, we reassess our own estimates for the Laplace pressure difference between water and vapour. These calculations are used to measure the disjoining pressure of premelting liquid films and allow us to confirm a minimum of the interfacial free energy at finite premelting thickness of about one nanometer.

Dewetting of a corner film wrapping a wall-mounted cylinder

In this study, we investigate the stability of a film that is attached to a corner between a cylinder and a substrate, using a combination of theoretical and numerical approaches. Notably, we place our focus on flat and thin films where the contact line is almost perpendicular to the cylinder wall whereas a small angle forms between the contact line and the substrate, and the film size is smaller than the cylinder radius. The film stability, which depends on the film size and the wall wettability, is first predicted by a standard linear stability analysis (LSA) within the long-wave theoretical framework. We find that the film size plays the most important role in controlling the film stability. Specifically, the thicker the film is, the less sensitive it becomes to the large-wavenumber perturbation. The wall wettability mainly impacts the growth rates of perturbations and slightly influences the marginal stability and postinstability patterns of wrapping films. We compare the LSA predictions with numerical results obtained from a disjoining pressure model (DPM) and volume-of-fluid (VOF) simulations, which provide more insights into the film breakup process. At the early stage there is a strong agreement between the LSA predictions and the DPM results. Notably, as the perturbation grows, thin film regions connecting two neighbouring satellite droplets form which may eventually lead to a stable or temporary secondary droplet, an aspect which the LSA is incapable of capturing. In addition, the VOF simulations suggest that beyond a critical film size, merging between two neighbouring drops becomes involved during the breakup stage. Therefore, the LSA predictions are able to provide only an upper limit on the final number of satellite droplets.

Condensation dynamics on inclined heterogeneous substrates

This study presents numerical simulations of dropwise condensation on inclined chemically heterogeneous substrates in pure vapor atmosphere. To capture the dynamics of this process, a one-sided condensation model with a disjoining pressure is employed that incorporates the effects of gravity and chemical heterogeneities. We consider surfaces decorated with an array of square patches which are more hydrophilic compared to the rest of the surface, which act as nucleation, inception regions over which droplets form and grow and ultimately depin once their size becomes sufficiently large. The impact of the size and of the inception regions and the angle of inclination on the dynamics is considered, revealing significant qualitative and quantitative differences between the cases. For cases with purely structured substrates, it is observed that, as the number of inception regions increases, the condensation process transitions from steady to unsteady, with the critical number of inception regions increasing with the inclination angle increases. Further insight is provided by analyzing the snapshots of the liquid phase on the substrate, revealing the formation of liquid streaks or films, which influence both the dynamics of the flow and the total liquid volume on the substrate. The inclusion of random impurities on the structured substrate dramatically impacts the condensation dynamics, which is found to hinder the formation of liquid film, leading to a decrease in the total liquid volume generated on the substrate.

What Drives Deformation of Smart Nanoporous Materials During Adsorption and Electrosorption?

Nanoporous solids have high surface area, so processes at the surface affect the sample as a whole. When guest species adsorb in nanopores, be they molecules adsorbing from the gas phase, or ions adsorbing from solution, they cause material deformation. While often undesired, adsorption- or electrosorption-induced deformation provides a potential for nanoporous materials to be used as actuators. Progress in this direction requires understanding the mechanisms of adsorption- or electrosorption-induced deformation. These two processes are rarely discussed together, and this Perspective aims to fill this gap to some extent, focusing on driving forces for both processes. Typically the main driving force for both is the solvation (disjoining) pressure, acting normally to the pore walls. However, in some cases, solvation pressure is not sufficient to describe the effects even qualitatively. We highlight examples in which the surface stress acting along the solid surface is an additional driving force for deformation.

Crude oil displacement enhanced by interfacially active nanoparticles and their coupling effect with low-salinity brines

From the microscopic scale to the petroleum-reservoir scale, the interfacial phenomena of a crude oil–water-rock system crucially control immiscible flow in a porous reservoir. One of the key mechanisms is crude oil droplet displacement dynamics, which can be optimized by manipulating the oil–water interfacial tension and the three-phase contact angle by means of chemical injection. Oil film displacement was enhanced by adding interfacially active nanoparticles, namely poly(N-isopropylacrylamide) or pNIPAM (43–48 nm hydrodynamic diameter and 0.0005–0.0050 wt% concentration range), accelerating the oil droplet receding rate (up to 5.66°/s) and greater degree of oil film dewetting (37.0° contact angle). Such behavior was attributed to nanoparticle-induced structural disjoining pressure between the oil–water and water–solid interfaces. The coupling effect of pNIPAM nanoparticles with low-salinity brines was studied, revealing discrepancy in different valency brines. Coupling with divalent CaCl2 led to much slower oil droplet receding dynamics (2.58°/s, and 58.7° contact angle) since oil-substrate bridging is formulated and promoted by the divalent cation. However, a positive synergy was observed with a monovalent NaCl blend. The crude oil dewetting dynamics were enhanced (9.55°/s) owing to the combined salt-induced hydration and nanoparticle-induced structural forces. The contact angle reduced to 21.5° before eventually detaching from the substrate after a relatively short period (156 s). These findings highlight the coupling effects of nanoparticles and low-salinity brine to enhance dewetting of heavy crude oil. Adding nanoparticles to an ‘optimal’ brine could be an option for faster and greater fluid displacement, which is not limited to oil production applications but several others, such as detergency and other forms of geological storage.

Visualizing oil displacement by nanofluids at pore scale: A concentration-dependent nanofluid spreading induced by structural disjoining pressure

Visualizing oil displacement by nanofluids at pore scale: A concentration-dependent nanofluid spreading induced by structural disjoining pressure

Hygroscopic Water Content As an Indicator of Soil Dispersity: Thermodynamic Basis and Experimental Verification

Abstract The adsorption properties of dispersed systems are determined by their surface energy, therefore the parameters of hygroscopy (adsorbed water content) and dispersity (specific surface area of the solid phase) of soils and sediments are in close mutual correlation. This well-known empirical fact has received a new fundamental interpretation based on the theory of disjoining water pressure according to Derjaguin should be in the form of a thermodynamic equation that connects the specific surface area, hygroscopic water content of soil samples, and relative air humidity in the laboratory room. The theoretical equation enables us to substantiate the methodology of quantifying the hydrophilic specific surface area of soil samples based on widespread data on their hygroscopy. Comparison of the new method with the standard BET analysis of the specific surface area, as well as with the previously proposed physically based method for its determining by the slope of thermodynamic water retention curves, shows their statistically reliable agreement in a wide range of the estimated specific surface area from 5 to 340 m2 g–1 for soil samples of different genesis and texture.

HYGROSCOPIC WATER CONTENT AS AN INDICATOR OF SOIL DISPERSITY:THERMODYNAMIC BASIS AND EXPERIMENTAL VERIFICATION

The adsorption properties of dispersed systems are determined by their surface energy, therefore the indicators of hygroscopy (adsorbed water content) and dispersity (specific surface area of the solid phase) of soils and sediments are in close mutual correlation. This well-known empirical fact received a new fundamental interpretation based on the theory of disjoining water pressure according to Deryagin in the form of a thermodynamic equation connecting the specific surface area, hygroscopic water content of soil samples and the relative humidity of the air in the laboratory room. The theoretical equation allowed us to substantiate the methodology for quantifying the hydrophilic specific surface area of soil samples based on widespread data on their hygroscopy. A comparison of the new method with the standard BET-analysis of the specific surface area, as well as with the previously proposed physically based method for its determining by the slope of thermodynamic water retention curves, showed their statistically reliable agreement in a wide range of estimated specific surface area values from 5 to 340 m2×g-1 for soil samples of different genesis and texture.

Quantifying Contributions of Different Repulsion to Film Drainage Time during the Bubble-Solid Surface Attachment and Implications for the Flotation of Fine Particles.

The flotation recovery of fine particles faces serious challenges due to the lack of kinetic energy required for supporting their radial displacement and attachment with bubbles. Generally, the hydrodynamic resistance and repulsive disjoining pressure successively inhibit the liquid outflow intervening between the bubble and solid surfaces. To quantitatively characterize the influence of the main repulsion on film thinning time, experiments have been designed in three different aqueous systems. Bubble surface mobility closely associated with hydrodynamic resistance was determined by the rising bubble technique, and the DLVO theory was employed to confirm the evolution of electrostatic repulsion. The film drainage process was then measured based on the high-speed microscopic interferometry. Furthermore, the influence of the main repulsion on bubble-solid surface interactions was examined by flotation recovery. Results show that the earlier buildup of hydrodynamic force ran through the whole film thinning process, and under immobile conditions, the central region gradually became dominant in film thinning due to the very limited fluid flow at the thinnest rim position. Therefore, to achieve the identical film thickness (∼100 nm), the large hydrodynamic resistance could prolong the film thinning time by about 1 order of magnitude, compared with that induced by electrostatic repulsion, which accounts for the increased flotation recovery by 10% using mobile bubbles. This study not only enhances the understanding of how typical repulsive forces work in film drainage dynamics but also opens up an avenue for enhancing flotation and avoiding wasting resources by modulating bubble surface mobility and thus micro/nanoscale fluid flow.

Capillary Condensation of Water in Graphene Nanocapillaries.

Recent experiments have revealed that the macroscopic Kelvin equation remains surprisingly accurate even for nanoscale capillaries. This phenomenon was so far explained by the oscillatory behavior of the solid-liquid interfacial free energy. We here demonstrate thermodynamic and capillarity inconsistencies with this explanation. After revising the Kelvin equation, we ascribe its validity at nanoscale confinement to the effect of disjoining pressure. To substantiate our hypothesis, we employed molecular dynamics simulations to evaluate interfacial heat transfer and wetting properties. Our assessments unveil a breakdown in a previously established proportionality between the work of adhesion and the Kapitza conductance at capillary heights below 1.3 nm, where the dominance of the work of adhesion shifts primarily from energy to entropy. Alternatively, the peak density of the initial water layer can effectively probe the work of adhesion. Unlike under bulk conditions, high confinement renders the work of adhesion entropically unfavorable.

Effect of equilibrium contact angle on water equilibrium film thickness for the carbon dioxide–brine–mineral system based on surface force theory

The thickness of the thin wetting film depends on disjoining pressure forces, and it evolves with pH evolution due to brine acidification at the physical and chemical conditions of geological carbon dioxide storage becoming thinner in response to dewetting. In the literature, molecular dynamic simulation (MDS) studies have been employed to understand the effect of pressure/capillary pressure on the thin wetting film evolution. In this paper, a theoretical approach based on the Frumkin–Derjaguin Equation (FDE), models of electric double layer repulsion, and van der Waals forces have been used for the calculation of the wetting film thickness. The approach excluded hydration forces contribution to disjoining pressure forces due partly to its poorly understood nature, and partly to the high salinity conditions encountered in geological carbon storage. Due to its promising global storage capacity compared to other lithologies, the carbon dioxide–brine–silica systems was chosen to simulate sandstone saline aquifers. The validation of the model benefited much from literature resources on data and a universal model of carbon dioxide–brine interfacial tension. Calculated results confirm pH-induced dewetting and they follow trends controlled by pH and pressure as found in the literature. The novelty of the paper can be seen from the fact that it has demonstrated a theoretical supplement to MDS studies in addition to justifying the fundamental utility and versatility of the FDE. Moreover, the paper links for the first time, a transcendental equation to the thin wetting film theory encountered in the carbon dioxide–solid–brine system found in geological carbon storage.

Toward Modeling the Structure of Electrolytes at Charged Mineral Interfaces Using Classical Density Functional Theory.

The organization of water molecules and ions between charged mineral surfaces determines the stability of colloidal suspensions and the strength of phase-separated particulate gels. In this article, we assemble a density functional that measures the free energy due to the interaction of water molecules and ions in electric double layers. The model accounts for the finite size of the particles using fundamental measure theory, hydrogen-bonding between water molecules using Wertheim's statistical association theory, long-range dispersion interactions using Barker and Henderson's high-temperature expansion, electrostatic correlations using a functionalized mean-spherical approximation, and Coulomb forces through the Poisson equation. These contributions are shown to produce highly correlated structures, aptly rendering the layering of counterions and co-ions at highly charged surfaces and permitting the solvation of ions and surfaces to be measured by a combination of short-range associations and long-ranged attractions. The model is tested in a planar geometry near soft, charged surfaces to reproduce the structure of water near graphene and mica. For mica surfaces, explicitly representing the density of the outer oxygen layer of the exposed silica tetrahedra allows water molecules to hydrogen-bond to the solid. When electrostatic interactions are included, water molecules assume a hybrid character, being accounted for implicitly in the dielectric constant but explicitly otherwise. The disjoining pressure between approaching like-charged surfaces is calculated, demonstrating the model's ability to probe pressure oscillations that arise during the expulsion of ions and water layers from the interfacial gap and predict strong interattractive stresses that form at narrow interfacial spacing when the surface charge is overscreened. This interattractive stress arises not due to in-plane correlations under strong electrostatic coupling but due to the out-of-plane structuring of associating ions and water molecules.

Peeling fingers in an elastic Hele-Shaw channel

Using experiments and a depth-averaged numerical model, we study instabilities of two-phase flows in a Hele-Shaw channel with an elastic upper boundary and a non-uniform cross-section prescribed by initial collapse. Experimentally, we find increasingly complex and unsteady modes of air-finger propagation as the dimensionless bubble speed $Ca$ and level of collapse are increased, including pointed fingers, indented fingers and the feathered modes first identified by Cuttle et al. (J. Fluid Mech., vol. 886, 2020, A20). By introducing a measure of the viscous contribution to finger propagation, we identify a $Ca$ threshold beyond which viscous forces are superseded by elastic effects. Quantitative prediction of this transition between ‘viscous’ and ‘elastic’ reopening regimes across levels of collapse establishes the fidelity of the numerical model. In the viscous regime, we recover the non-monotonic dependence on $Ca$ of the finger pressure, which is characteristic of benchtop models of airway reopening. To explore the elastic regime numerically, we extend the depth-averaged model introduced by Fontana et al. (J. Fluid Mech., vol. 916, 2021, A27) to include an artificial disjoining pressure that prevents the unphysical self-intersection of the interface. Using time simulations, we capture for the first time the majority of experimental finger dynamics, including feathered modes. We show that these disordered states evolve continually, with no evidence of convergence to steady or periodic states. We find that the steady bifurcation structure satisfactorily predicts the bubble pressure as a function of $Ca$ , but that it does not provide sufficient information to predict the transition to unsteady dynamics that appears strongly nonlinear.